Question

If \( \sin \theta = \frac{3}{5} \), find the value of \( \cos \theta \).

• A. \( \frac{4}{5} \)
• B. \( \frac{2}{5} \)
• C. \( \frac{3}{5} \)
• D. \( \frac{1}{5} \)

Hint:

Use the Pythagorean identity \( \sin^2 \theta + \cos^2 \theta = 1 \) to find missing trigonometric values.

Answer 1

The Correct Option is A

We know that: \[ \sin^2 \theta + \cos^2 \theta = 1 \] Given \( \sin \theta = \frac{3}{5} \), we can substitute into the equation: \[ \left( \frac{3}{5} \right)^2 + \cos^2 \theta = 1 \] \[ \frac{9}{25} + \cos^2 \theta = 1 \] \[ \cos^2 \theta = 1 - \frac{9}{25} = \frac{25}{25} - \frac{9}{25} = \frac{16}{25} \] \[ \cos \theta = \frac{4}{5} \] Thus, the value of \( \cos \theta \) is \( \frac{4}{5} \). Therefore, the correct answer is option (1).